Inference on parameter β of the Generalized Negative Binomial Distribution


Abstract


In this paper, we propose a generalized likelihood ratio test to discern
whether a set of data fits a Negative Binomial as a particular case of the
Generalized Negative Binomial Distribution(GNBD). The test attempts to
differentiate the GNBD from Negative Binomial (NBD) distribution when
fitting discrete data. A Monte Carlo simulation study was performed to investigate the power and the size of the proposed test, and results shows good performance in power and size under moderate sample sizes of the LRT test for testing hypotheses on parameter β of the Generalized Negative Binomial Distribution. A Parametric Bootstrap for investigating the distribution of parameter β of the GNBD and a Bayesian approach for obtaining the posterior distribution of the GNBD parameters were also implemented. In order to illustrate the proposed methodology, we included two cases: a dataset of an entomological study on mosquitoes of malaria and another study on species of Malaysian butterflies.

DOI Code: 10.1285/i20705948v15n1p26

Keywords: Bootstrap, discrete distributions, count data, hypothesis testing, simulation.

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